You see that the two numbers 3.1416 and 22/7 are both close to Pi and
to each other in value.
The actual circumference of a 10 foot diameter circle is 10*Pi feet,
or about 31.4159265 feet, or 31 feet 4.991118 inches. If you use
10*3.1416 = 31.416 feet, you get 31 feet 4.992 inches. These answers
differ by only 0.000882 inches -- very close! If you use instead
10*22/7 = 31.4285714 feet, you get 31 feet 5.142857 inches. These
answers differ by 0.1517387 inches, or about 5/32 inches. That isn't
bad, either.
The result of this analysis is that for most purposes, 22/7 is a
pretty good estimate of Pi (three significant figures), and 3.1416 is
better (five significant figures), but if you need very high accuracy,
you should use an even more accurate estimate of Pi. Decide what
accuracy you need, and round the value of Pi to that many significant
figures. Then use that times the diameter to get the circumference.
